FOM: Re: Copernicus and Newton -- empty space

[Mark Steiner]

I apologize for my earlier posting which was sent by mistake in draft form.
Though I don't have time now to check the reference, Newton explicitly
disqualifies plane orbital motion where the force vectors converge on empty
space.  "Luckily," the Keplerian laws have the sun right there at the focus of
the ellipse, upon which the Newtonian force vectors, required by those laws,
converge.  He also shows, using one of the first theorems of Principia, namely
that in circular motion the force vector is as v^2/R, that the Ptolemaic
hypothesis implies that the earth exerts a force that increases with the
distance, an impossibility.  Incidentally, I don't want to get into the
"intuition vs. rigor" controversy, but one could plausibly argue that what is
called "physical intuition" as well as rigor is at work here, since the
principles involving the nature of force are never really set down as axioms by
Newton.

By thinking dynamically, Newton thus demolished in one sentence what took
Galileo three books and house arrest to do.  As my colleague in Tel-Aviv Rivka
Feldhai has recently shown, the Catholic Church, after trying Galileo for
Copernicanism, undermined their own position by funding research in dynamical
theory which brought an end to all geocentric theories.



José Félix Costa wrote:

> Mark wrotes:
>
> ''empty absolute space (though it does exist for Newton) cannot exert
> forces''
>
> This is not quite true for Newton...
> Empty space is the space of Democritus and Leucipus and the space of
> empirists after Newton.
> Cartesian and Leibnizian space is substancial and Newton's space is
> SENSORIUM DEI
> the place of God's sensations.
> You can read in Optics that God perceives things through space and remove
> gravitational instabilities (Newton was afraid of the colapse of the
> Universe and in Optics postulated a God with action in every moment opposite
> to Lebnizian God -- the God of Shabbat). In this sense the space of Newton
> do exert forces.
>
> Felix
>
> +++++++++++++++++++++++++++++++++++++++++++++++
> J. Felix Costa
> Departamento de Matematica
> Instituto Superior Tecnico
> Av. Rovisco Pais, 1049-001 Lisboa, PORTUGAL
> tel:      351 - 21 - 841 71 45
> fax:     351 - 21 - 841 75 98
> e-mail:   fgc at math.ist.utl.pt
> www:    http://www.cs.math.ist.utl.pt/cs/fgc.html
> +++++++++++++++++++++++++++++++++++++++++++++++